The objective of the proposed research is to develop theory and methods for testing for sufficient cause inter- actions. The methods will be useful in identifying mechanistic interactions in biological systems and in and in the analysis and interpretation of studies in genetic epidemiology of gene-gene and gene-environment interactions. It is well known both that the presence of an interaction in a statistical model depends on the model being employed and furthermore that a statistical interaction need not correspond to an interaction in any biologically or physically meaningful sense. The sufficient cause framework makes reference to the actual causal mechanisms, referred to as sufficient causes, involved in bringing about the outcome. When two or more binary causes participate in the same causal mechanism, synergism is said to be present. Sometimes synergism cannot be identified from data; when data do imply that synergism must be present then a sufficient cause interaction is said to be present. The theory and methods developed through the proposed research lead to empirical tests for sufficient cause interactions and thus constitute tests for the joint presence of two or more causes in a single causal mechanism. The aims of the research are to extend the theory concerning the sufficient cause framework for dichotomous exposures, to develop theory for sufficient cause interaction for ordinal and categorical exposures, to develop multiply robust semiparametric tests for the presence of sufficient cause interactions, and to characterize those forms of exposure misclassification for which tests for sufficient cause interactions yield valid conclusions. The research will provide a set of techniques that can be used to identify mechanistic interactions in biological systems and will develop both a theoretical framework in which to conceptualize these mechanistic interactions and provide methods to empirically test for such interactions. The research will be useful in identifying mechanistic gene-gene and gene-environment interactions which could increase our understanding of genetic mechanisms. The implications of the research on sufficient cause interactions for understanding the mechanistic implications of standard gene-gene and gene-environment interaction tests and study designs will be explored and the methods developed will be applied to several data sets in the Health Effects of Arsenic Longitudinal Study. The research will make important advances to the statistical literature on the concept of interaction and on the implications of measurement error for causal inference. The overall research program will contribute to our understanding of the concepts of causation which form the foundation of the statistical literature in causal inference and which are being employed in medicine, epidemiology, psychology, genetics, computer science, philosophy, sociology, education and economics.